Having taken one point from matches against Villarreal and Real Sociedad since the winter break, Los Che needed a win on Sunday to have any chance of keeping in touch with La Liga's leading pair, Real Madrid and Barcelona.
They appeared to be on their way when Roberto Soldado gave them a scarcely deserved lead in the 85th minute, but Valencia self-destructed in stoppage time as David Albelda was sent off and Lolo levelled from the resulting free-kick.
A victory would have been more than Valencia deserved as they struggled to create chances against a team who went into the game with the joint second worst defence in the league.
Indeed, they rarely got a sight at goal and were restricted for the most part to long-range efforts.
The first of those fell to Jonas, who set the tone by firing over from 25 yards.
Another half-chance fell to Sofiane Feghouli after Tino Costa's corner broke to him on the edge of the area, but he too could not keep his effort down.
Soldado got a better sight of goal after 23 minutes but even from much closer range he could not find the target, firing wide.
Osasuna started to threaten as half-time loomed, with Roland Lamah firing straight at Diego Alves from 25 yards and Javad Nekounam sending his shot wide from a similar distance.
And they maintained their improvement after the restart when Raul Garcia brought a decent save out of Alves.
He got his head to a corner from Alvaro Cejudo in the 51st minute and Alves had to turn the ball behind.
Alves had to be on hand again two minutes later when Nekounam's 25-yard free-kick was on target.
The match appeared to be fizzling out before a hectic final six minutes.
Soldado seemed to have given Valencia a smash-and-grab win when he headed home Costa's cross.
But Albelda fouled David Timor, earning a straight red, and Alves parried the resulting free-kick from Cejudo, allowing substitute Lolo to level from close range.